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- W1566953979 abstract "Given a complex- or real-analytic variety Y (or an algebraic variety Y over a field of characteristic zero), can we find a global resolution of singularities s: X -> Y such that the pulled-back cotangent sheaf of Y is generated by differential monomials in suitable coordinates at every point of X coordinates)? We prove that the answer is yes in dimension up to three. It was previously known for surfaces with isolated singularities (Hsiang-Pati 1985, Pardon-Stern 2001). Consequences include monomialization of the induced Fubini-Study metric on the smooth part of a complex projective variety Y; there have been important applications of the latter to L2-cohomology. Existence of Hsiang-Pati coordinates is equivalent to monomialization of Fitting ideals generated by minors of a given order of the logarithmic Jacobian matrix of s." @default.
- W1566953979 created "2016-06-24" @default.
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- W1566953979 date "2015-04-27" @default.
- W1566953979 modified "2023-09-27" @default.
- W1566953979 title "Hsiang-Pati coordinates" @default.
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